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Asymptotic results for a barrier potential model

Published online by Cambridge University Press:  15 May 2015

DAVID A. EDWARDS  and
CHRISTOPHER S. RAYMOND
DAVID A. EDWARDS
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE, USA email: dedwards@udel.edu, craymond@udel.edu
CHRISTOPHER S. RAYMOND
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE, USA email: dedwards@udel.edu, craymond@udel.edu
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Abstract

An enhanced understanding of the microstructure of oxide ceramics will help scientists and engineers improve their efficiency and design. A phase-field model for the composition and phase distribution of the oxide ceramic components is studied. The model, which includes an obstacle in the phase portion of the energy potential, results in a minimisation problem that characterises the distribution of the bulk phases. The transition region between them is studied in several mathematically plausible asymptotic limits. The behaviour of the system in these limits provides insights into the applicability of the model and indicates appropriate parameter regimes.

Keywords

Phase-field modelAsymptoticsOxide ceramics
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 6 , December 2015 , pp. 863 - 886
Copyright
Copyright © Cambridge University Press 2015 

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